The round complexity of verifiable secret sharing (VSS) schemes has been studied extensively for threshold adversaries. In particular, Fitzi et al. showed an efficient 3-round VSS for n ≥ 3t+1 [4], where an infinitely powerful adversary can corrupt t (or less) parties out of n parties. This paper shows that for non-threshold adversaries, 1. Two round VSS is possible iff the underlying adversary...

In this work we provide efficient distributed protocols for generating shares of random noise, secure against malicious participants. The purpose of the noise generation is to create a distributed implementation of the privacy-preserving statistical databases described in recent papers [14, 4, 13]. In these databases, privacy is obtained by perturbing the true answer to a database query by the ...

In a threshold scheme, the sensitivity of the secret as well as the number of players may fluctuate due to various reasons, e.g., mutual trust may vary or the structure of the players’ organization might be changed. A possible solution to this problem is to modify the threshold and/or change the secret. Moreover, a common problem with almost all secret sharing schemes is that they are “one-time...

In this paper, we investigate how to achieve verifiable secret sharing (VSS) schemes by using the Chinese Remainder Theorem (CRT). We first show that two schemes proposed earlier are not secure by an attack where the dealer is able to distribute inconsistent shares to the users. Then we propose a new VSS scheme based on the CRT and prove its security. Using the proposed VSS scheme, we develop a...

In a (t,n) secret sharing scheme, a mutually trusted dealer divides a secret into n shares in such a way that any t or more than t shares can reconstruct the secret, but fewer than t shares cannot reconstruct the secret. When there is no mutually trusted dealer, a (n,t,n) secret sharing scheme can be used to set up a (t,n) secret sharing because each shareholder also acts as a dealer to decide ...

Verifiable secret sharing is a cryptographic primitive used in many distributed applications. To engineer realistic applications, it is beneficial to have dynamically changing shares and shareholder groups. Proactive secret sharing schemes deal with dynamically changing shares. Secret redistribution schemes solve issues of both dynamically changing shares and shareholder groups. In this dissert...

In this paper, we first propose a protocol in which the prover can show that a = b holds for two committed integers a and b; also, we present a protocol in which the prover can prove that a 6= 0 holds for committed integer a; then, we construct a protocol to prove that the degree of a polynomial f(x) equals to t− 1 exactly, which has been as an open problem(see[21]); finally, we provide a proto...

In secret sharing scheme, the master secret and all the private shares (which are distributed by the dealer to the shareholders) are the two secrets which are to be maintained confidentially. In all the secret sharing schemes proposed till date, private shares are reused to reconstruct the master secret. But we proposed a new way of Proactive Secret Sharing Scheme in which, instead of renewing ...

This paper presents a non-interactive verifiable secret sharing scheme (VSS) tolerating a dishonest majority based on data predistributed by a trusted authority. As an application of this VSS scheme we present very efficient unconditionally secure multiparty protocols based on pre-distributed data which generalize two-party computations based on linear pre-distributed bit commitments. The main ...

We present new cryptographic protocols for multi-authority secret ballot elections that guarantee privacy, robustness, and universal verifiability. Application of some novel techniques, in particular the construction of witness hiding/indistinguishable protocols from Cramer, Damg̊ard and Schoenmakers, and the verifiable secret sharing scheme of Pedersen, reduce the work required by the voter or ...